Exterior Angle of Cyclic Quadrilateral

Q.

In the given figure, $\angle A={60}^{\circ }$ and $\angle ABC={80}^{\circ }$, then $\angle DPC$ and $\angle BQC$ are respectively ___.

1. ${60}^{\circ },{30}^{\circ }$

2. ${40}^{\circ },{40}^{\circ }$

3. ${40}^{\circ },{20}^{\circ }$

4. ${20}^{\circ },{60}^{\circ }$

Q.

In the given figure, if $\angle \text{OAB}={40}^{\circ }$, then $\angle \text{ACB}$ = ___.

1. ${50}^{\circ }$

2. ${40}^{\circ }$

3. ${60}^{\circ }$

4. ${70}^{\circ }$

Q.

In the given figure, chords $AB=CD,\angle COD={60}^{\circ }$ and $\angle AOD={170}^{\circ }$.

Find the value of $\angle BOC$.

1. ${60}^{\circ }$

2. ${70}^{\circ }$

3. ${75}^{\circ }$

4. ${80}^{\circ }$

Q.

The number of equal angles an arc subtends in the opposite segment is _______.

1. two

2. four

3. none
4. infinite

Q. In the given figure, O is the centre of the circle. If $\angle BOC={120}^{\circ },$ then $x$ =___.

1. ${40}^{\circ }$​​​​​​​
2. ${30}^{\circ }$​​​​​​​
3. ${45}^{\circ }$​​​​​​​
4. ${60}^{\circ }$

Q.
If $\angle BCD={50}^{\circ },$ then $\angle BAD$ = ___.

1. ${50}^{\circ }$
2. ${100}^{\circ }$
3. ${25}^{\circ }$
4. ${70}^{\circ }$

Q.

ABCD is a cyclic quadrilateral. If $\angle BCD={100}^{\circ }$ and $\angle ABD={70}^{\circ },$ then find $\angle ADB.$

1. ${30}^{\circ }$
2. ${40}^{\circ }$
3. ${50}^{\circ }$
4. ${60}^{\circ }$

Q. In the given figure, AC is a diameter of the circle. Find the value of $x.$

1. ${136}^{\circ }$
2. ${100}^{\circ }$
3. ${126}^{\circ }$
4. ${154}^{\circ }$

Q.

Consider the cyclic quadrilateral ABCD. If O is the centre of the circle and $\angle$BOD = ${160}^{\circ }$, then find the measure of $\angle$BPD.

1. ${100}^{\circ }$

2. ${80}^{\circ }$

3. ${90}^{\circ }$

4. ${70}^{\circ }$

Q. ABCD is a cyclic quadrilateral whose diagonals intersect at a point E. If $\angle DBC={80}^{\circ },\angle BAC$ is ${40}^{\circ },$ find $\angle BCD$.

1. ${60}^{\circ }$
2. ${80}^{\circ }$
3. ${50}^{\circ }$
4. ${40}^{\circ }$